We study strategic reasoning and the beliefs people form about the beliefs of others in the presence of private information. We find that while people naively project and think others have the same information as they do, they also anticipate the analogous projection of their differentially-informed opponents onto them. In turn, the typical person explicitly thinks that others form systematically biased beliefs. Specifically, our paper directly tests the model of projection equilibrium, Madarasz (2014, revised 2016), which posits a parsimonious one-to-one relationship between the partial extent to which a player projects and forms biased beliefs about the beliefs others,?, and the partial extent to which she anticipates but underestimate the same systematic bias in others' beliefs of her beliefs,?²². We find that the distribution of the partial extent to which players project onto others and the distribution of the partial extent to which they anticipate others' projection onto them is remarkably consistent with the tight link implied by the model.